Graphite covalent energy

The electronic structure in graphite may be understood in terms o(sp hybrids (see Problem 3-2) oriented in the direction of the bond and bond orbitals constructed from these hybrids. The shorter bond length and different composition of the hybrid lead to a covalent energy value, Fj. that is also different in graphite than it is in diamond. 

Rederive an expression for the covalent energy (sec Eq. 4-18) for the graphite structure, and evaluate the corresponding polarity for hexagonal BN, assuming that it has the graphite bond length (see Problem 3-1). 

For an element that occurs in different forms (allotropcs), the entropy is higher in the form that allows the atoms more freedom of motion, which disperses their energy over more microstates. For example, the S° of graphite is 5.69 J/mol-K, whereas the S° of diamond is 2.44 J/moFK. In diamond, covalent bonds extend in three dimensions, allowing the atoms little movement in graphite, covalent bonds extend only within a two-dimensional sheet, and motion of the sheets relative to each other is relatively easy. 

Network solids such as diamond, graphite, or silica cannot dissolve without breaking covalent chemical bonds. Because intermolecular forces of attraction are always much weaker than covalent bonds, solvent-solute interactions are never strong enough to offset the energy cost of breaking bonds. Covalent solids are insoluble in all solvents. Although they may react with specific liquids or vapors, covalent solids will not dissolve in solvents. 

The problem of recovery leads to the question of hardness. Hard substances have a high number of strongly directed, covalent chemical bonds per unit volume. Soft substances generally have fewer bonds per unit volume or bonds that are weak or weakly directed, such as ionic or dipole attractive forces. Bond energy per unit volume has the same dimensions as pressure (force per unit area), and a plot of hardness measured by the Knoop indenter versus the bond energy per molar volume for various substances is essentially linear, provided that one chooses substances for which the bonding is predominantly of one type (i.e., not mixed, as in graphite or talc). 

The same can be done in the graphite lattice as show in Fig. 2. The bonding force acting between two neighboring atoms can be directly demonstrated as a function of interatomic separation, resulting in anisotropic properties. The bond energy in the c direction is commonly called van der Waals bond or n electron interaction and is estimated to be 17-33 kJ/mol between the planes as compared to 430 kJ/mol of chemical covalent nature or tr-bond within the planes [37]. 

Consider hexagonal boron nitride, shown in Fig. 3-10. Define a hybrid covalent and hybrid polar energy for this structure, in analogy with the corresponding definitions for tetrahedral solids in Eqs. (3-4) and (3-6). Compare the polarity obtained from these values with that of tetrahedral BN, listed in Table 7-2. Take d = 1.42 A as in graphite. Notice that many values arc modified by having sp hybrids rather than sp hybrids. 

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